Best Known (102, 102+∞, s)-Nets in Base 9
(102, 102+∞, 222)-Net over F9 — Constructive and digital
Digital (102, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (102, 221)-sequence over F9, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
(102, 102+∞, 275)-Net over F9 — Digital
Digital (102, m, 275)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (102, 274)-sequence over F9, using
- t-expansion [i] based on digital (101, 274)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 101 and N(F) ≥ 275, using
- t-expansion [i] based on digital (101, 274)-sequence over F9, using
(102, 102+∞, 844)-Net in Base 9 — Upper bound on s
There is no (102, m, 845)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (102, 2531, 845)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92531, 845, S9, 3, 2429), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1997 540857 637854 690572 338211 866216 632629 950303 912618 918167 221859 225927 527132 452600 443392 891286 050029 568743 495790 017168 761015 748935 230757 267269 515207 151044 300774 264508 857566 793459 629304 463753 668026 526375 569745 782227 529995 773362 048351 648460 498943 385151 353566 141964 223003 702796 847920 517884 032692 704768 568849 197759 186412 634272 099984 471302 891606 425887 055997 625080 137888 652198 231615 610916 107936 081399 502234 475187 249702 320993 491949 617216 526131 286127 516212 274021 155293 448738 634510 091302 046484 462577 276696 506414 846400 442467 478501 886890 071888 748783 219035 433751 834443 582642 471115 966926 923015 070632 657453 120059 345334 843649 807813 040482 149470 648580 165804 052598 575495 767114 273209 986295 172054 869460 152982 017861 271507 536620 829245 043588 244824 562384 778817 310954 537934 058813 775882 078052 381819 408245 669790 956829 183751 134780 229550 044759 374637 946963 103446 839075 130009 525168 375777 342662 808931 189435 497858 080985 954516 796049 011019 366962 430538 521980 459701 035725 528291 865346 479737 407254 308601 473342 513047 032739 115711 186111 130418 269657 491122 724848 320951 199283 164288 955958 114092 940516 005505 425291 870516 829886 335905 419587 913276 563468 383381 833395 194501 015747 433665 315299 518839 202232 925325 648591 906646 184661 908662 561792 143454 752035 580195 620605 871447 714624 272697 838374 394824 477308 610174 357480 431128 782140 785115 532757 102181 311884 317300 654520 191631 440175 344524 860900 471522 472263 559292 499635 116533 964455 950952 110861 269488 607191 815155 540840 287045 165453 441373 013138 479985 286516 560906 112842 888874 054252 664825 744653 241180 141685 836498 820290 966859 765291 506005 422841 837420 764116 891703 414016 905532 267258 580993 239344 389205 574915 659382 686996 156098 365713 005398 406932 366947 850264 588666 429020 040508 291300 584419 483931 305165 390190 360436 652442 771322 080926 279749 784768 264143 986774 555899 083904 794862 900657 539823 455872 347142 116571 737000 022721 466566 224872 515880 632736 005621 675376 715251 043307 246420 697927 467437 338024 323756 962686 570766 920121 024676 274597 843960 039525 648940 457689 860309 713848 549838 875022 211919 392255 323406 212477 674866 485868 604421 102683 824114 773476 021119 794537 448477 488375 273301 456211 432439 970380 957124 157504 899375 864088 979654 241132 489786 960039 800847 492055 161627 324316 478590 278061 715282 895922 266809 066253 594409 335274 488235 616597 135392 576229 473720 879876 279803 579956 537531 456862 681980 247059 091628 394892 851426 544149 408207 951092 392225 298737 484357 357764 399012 748050 696751 302326 607054 646972 041194 583804 395750 687789 844551 744051 319403 783332 197317 269193 414949 722722 887345 > 92531 [i]
- extracting embedded OOA [i] would yield OOA(92531, 845, S9, 3, 2429), but